(CNN) -- Amid conservative opposition, a bill that would designate a day of "significance" in California for slain gay politician Harvey Milk is heading to Gov. Arnold Schwarzenegger's desk.

Harvey Milk was California's first openly gay elected official. He was assassinated in 1978.

The legislation would denote May 22 -- Milk's birthday -- as a day of significance across the state.

The governor's office said Tuesday it had received more than 100,000 constituent phone calls about the bill, although it was not immediately clear if most were in favor of it or opposed. The governor's office said Schwarzenegger has not taken a position on it yet.

Milk, the state's first openly gay elected official, served briefly as San Francisco's supervisor before he and Mayor George Moscone were assassinated in 1978.

Schwarzenegger vetoed a similar bill last year, saying he believed Milk "should be continued to be recognized at the local level by those who were most impacted by his contributions."

State Sen. Mark Leno, a Democrat who authored the current bill as well as last year's, said in a written statement that the governor had "contradicted" his veto message by announcing that the gay rights icon will be inducted into the California Hall of Fame.

Milk was a "unique" historical figure who led a civil rights movement and then was "assassinated in his public office for being who he was," Leno said.

Don't Miss

"In a perfect world, we'd have a state holiday for him, like [the Rev.] Martin Luther King Jr. or Cesar Chavez," Leno said in a telephone interview.

But the California state finances are in such "disarray ... we think it's appropriate in light of our fiscal crisis" to have a special day of significance that won't cost the state anything, said Leno, whose district includes portions of San Francisco.

That way, he said, Milk is still afforded "the respect that he's due."

The day of significance would not close schools or state offices, according to its text.

However, Randy Thomasson, the president of SaveCalifornia.com, said the bill was vague and could allow for a number of things at schools, including gay pride parades or "mock gay weddings."

"There's no definition in the bill," he said. "There is absolutely no limit to what could occur on campuses and go into little children's brains."

"Harvey Milk was a terrible role model for children," Thomasson said. His organization plans to oppose the bill through automatic phone calls, e-mails, media interviews and news conferences, he added.

Leno said that claims that the bill would lead to schools holding gay-pride parades and similar activities were "hyperbole."

The bill "mandates nothing," he said, although it certainly "affords an educational opportunity."

President Obama also posthumously honored Milk with a Presidential Medal of Freedom this year, and Sean Penn portrayed him in this year's film "Milk," which garnered him an Oscar for best actor.